### The conditions of existing integrals system equations of motion

#### A. V. Zubov^{1}, A. F. Zubova^{2}, O. A. Pustovalova^{3}

Annotation | In giving work is receives analog know theorem Haritonov's on case homogeneous classes of equivalent instability interval polynomials. V.L. Haritonov is installs that for stability interval polynomial necessary and sufficiently that four this angle polynomial was stabilizes. The base result own investigations is contains in that is gives necessary and sufficiently conditions that instability interval polynomial is appears homogeneous, i.e. is consists from polynomials is have equal number roots is lies as in left, so in right half-plane. Is giving conditions several composite, than by V.L. Haritonov, but they is allows so as in case stability polynomials, infinitely measure task is reduces to last measure task. |
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Keywords | Polynomial, degree, material coefficient, root, class of equivalent, rectangle, radius - vector, integrated plane, parallel axis, hands of a clock |

^{1}Docent chair theory of control; SPbGU, t. Saint-Petersburg; ddemidova@mail.ru^{2}Professor chair theory of control; SPbGU, t. Saint-Petersburg; ddemidova@mail.ru^{3}Docent chair theory of control; SPbGU, t. Saint-Petersburg; ddemidova@mail.ru

**Citation**: A. V. Zubov , A. F. Zubova , O. A. Pustovalova , "[The conditions of existing integrals system equations of motion]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:1 (2015) 140–144 (In Russian)